Mini-Workshop: Adaptive Methods for Control Problems Constrained by Time-Dependent PDEs

  • Max Gunzburger

    Florida State University, Tallahassee, USA
  • Karl Kunisch

    Karl-Franzens-Universität Graz, Austria
  • Angela Kunoth

    Universität zu Köln, Germany

Abstract

Optimization problems constrained by time-dependent PDEs (Partial Differential Equations) are challenging from a computational point of view: even in the simplest case, one needs to solve a system of PDEs coupled globally in time and space for the unknown solutions (the state, the costate and the control of the system). Typical and practically relevant examples are the control of nonlinear heat equations as they appear in laser hardening or the thermic control of flow problems (Boussinesq equations). Specifically for PDEs with a long time horizon, conventional time-stepping methods require an enormous storage of the respective other variables. In contrast, adaptive methods aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities and are, therefore, most promising.

Cite this article

Max Gunzburger, Karl Kunisch, Angela Kunoth, Mini-Workshop: Adaptive Methods for Control Problems Constrained by Time-Dependent PDEs. Oberwolfach Rep. 14 (2017), no. 1, pp. 167–211

DOI 10.4171/OWR/2017/4